harmonic minor scale
The harmonic minor group of pitches is comprised of a cool combination of colors. A close relative of the natural minor, the harmonic minor grouping of pitches is unique in that there are three half steps in its intervalic construction. From the below chart we see that the pitches of the two groups are identical excepting the 7th scale degree, which is raised a half step up, creating the leading tone pitch as usually found on in the major scale group of pitches. Comparing the natural and harmonic minor groups using A as the root. Example 1.
|scale degree / interval||1 / root||2 / major 2nd||3 / minor 3rd||4 / perfect 4th||5 / perfect 5th||6 / minor 6th||7 / major 7th||8 / octave|
|natural minor scale||A||B||C||D||E||F||G||A|
|harmonic minor scale||A||B||C||D||E||F||G#||A|
As the above chart shows, the pitches of these two groups are nearly identical. The essential minor third interval above the root is present, creating an overall minor tonal environment. The uniqueness of the harmonic minor color is that it combines the minor third with the major seventh. Over the years I've heard the harmonic minor group of pitches also described as the "Hungarian" or "gypsy minor scale" because of it's distinct, ancient cultural flavor, associated with the people of that European region and their traditions. This group of pitches goes way back in history, try this lick with lots of vibrato. Example 1a.
A bit different eh? But cool perhaps in that this musical phrase uses the three half step intervals which helps define the harmonic minor group. The half step resolution to the tonic in bar 4 becomes a reasonably radical departure from the sound of the minor seventh of the natural minor group.
So why is this group important? Well, standing alone, the harmonic minor grouping of pitches is a very strong, definable and historically significant color. There is an ancient European culture that uses this group and variations thereof as the center of their musical universe. The above configuration is the way that it comes into the world of equal temperament, but the only way to hear how the pitches and the resulting music sound is to go to the music. Part Gypsy, part Klezmer (?), look for recordings wherever you can. Lest we forget in our listening that much of our American, musical world is "equal tempered", where many of the tuning concerns are "adjusted." Secondly, that when used in conjunction with the natural minor group, the harmonic minor group expands the resource with the addition of the major seventh, an important pitch in regards to tonal gravity, both melodically and harmonically. This simple expansion of the resource adds another artistic and potentially very intense emotional dimension to the minor tonal environment.
Harmonically, the addition of the leading tone into the minor tonal environment as provided by the harmonic minor scale creates a situation where the chord built on the fifth scale degree, the dominant chord, evolves from a minor triad to a major triad. A simple shifting of pitches creates a much stronger cadential motion. Example 2.
|without leading tone||with leading tone|
Are you hip to spelling chords? A second important contribution from the harmonic minor grouping of pitches is termed the fully diminished seventh chord / arpeggio. Let's explore. Here is the harmonic minor scale as presented above then rewritten in its arpeggiated form. Example 3.
|harmonic minor scale||A||B||C||D||E||F||G#||A|
|harmonic minor arpeggio||A||C||E||G#||B||D||F||A|
So where is the fully diminished chord? Hint, its located in the harmonic minor arpeggio. Need another hint? Okay. Can you find three consecutive minor third intervals? See it, cool, it starts on the leading tone G#, which becomes the root of the chord. Three consecutive minor thirds? Here's a chart. Example 3a.
|interval from root||root||minor third||minor third||minor third|
Hip to the sound of the diminished color? Check it out moving to first the minor then major tonalities. Example 3b.
Pretty harsh eh? Oh well, it never gets to be the tonic anyway. So why is this harsh and dissonant diminished color potentially so important? Well, for a number of reasons. Again, the idea that "how important" is really an individual thing. Although very rare in folk, rock and even blues music, the diminished color is an important component in jazz harmony. Especially in standards, where it is perhaps the ultimate passing chord of all time. Why? Well, as G# is the leading tone of the major and minor tonality associated with the key of A, it turns out that the other pitches of the fully diminished chord are also leading tones to other keys. Really? Yes. So, the one fully diminished chord can actually resolve to four different tonal centers or tonics? Yep. Perhaps this is why this color is potentially the ultimate passing chord? Here is the sound of the one fully diminished color built on the root G# resolving to four different minor tonics. Example 3c.
|A minor||C minor||Eb minor||Gb minor|
What about the relative major tonalities of the four keys from example 3c? Sure why not. Example 3d.
|A major||C major||Eb major||Gb major|
Needless to say, we are barely scratching the surface of the theoretical discussion of the diminished color here, but please realize that only from within the harmonic minor group can we diatonically derive the diminished color, excepting of course the chromatic scale, but we can derive all of our equal tempered colors are contained within the chromatic group, right? Right. So this "scratch" is just for the record so to speak, to look at the diminished colors "organic" origin from harmonic minor and arouse a bit of curiosity perhaps. The real discussion of this important color and its resolving potentials fully takes place in the improvisation section. Go there now if your curious about the "harsh" color that can potentially work so many gorgeous wonders.
Back to basics, here is the harmonic minor color created from the 12 different pitches of the chromatic scale, sequenced by the cycle of fourths. Example 4.
|scale degree / interval||1 / tonic||2 / major 2nd||3 / minor 3rd||4 / perfect 4th||5 / perfect 5th||6 / minor 6th||7 / major 7th||8 / octave|
|C har. minor||C||D||Eb||F||G||Ab||B||C|
|G har. minor||G||A||Bb||C||D||Eb||F#||G|
|D har. minor||D||E||F||G||A||Bb||C#||D|
|A har. minor||A||B||C||D||E||F||G#||A|
|E har. minor||E||F#||G||A||B||C||D#||E|
|B har. minor||B||C#||D||E||F#||G||A#||B|
|F# har. minor||F#||G#||A||B||C#||D||E#||F#|
|Db har. minor||Db||Eb||Fb||Gb||Ab||Bbb (A)||C||Db|
|Ab har. minor||Ab||Bb||Cb||Db||Eb||Fb (E)||G||Ab|
|Eb har. minor||Eb||F||Gb||Ab||Bb||Cb (B)||D||Eb|
|Bb har. minor||Bb||C||Db||Eb||F||Gb||A||Bb|
|F har. minor||F||G||Ab||Bb||C||Db||E||F|
Here are the above 12 harmonic minor scales written out in standard musical notation. Things get a bit tricky accidental wise, work carefully. Same format as above. Example 4a.
|A harmonic minor|
|D harmonic minor|
|G harmonic minor|
|C harmonic minor|
|F harmonic minor|
|Bb harmonic minor|
|Eb harmonic minor|
|Ab harmonic minor|
|C# harmonic minor|
|F# harmonic minor|
|B harmonic minor|
|E harmonic minor|
Here is the extended version for shedding the harmonic minor color for one key. Try to adapt this shaping of the line to the other 11 keys, do it from memory and gradually over the years extend the range of the melodic minor color throughout your horn. Example 5.
Here is a twenty four bar "tour" of the 12 harmonic minor keys, moving one, two bar melodic idea around the cycle of fourths starting on C. Watch for enharmonic keys. Example 6.
The following tune, "Bluer Than Black", by the author, features a first theme created with the harmonic minor color, contrasted with the major tonality in the second theme. At 200 m.m. or so, here is the music. Example 7.
"Bluer Than Black" composed by Joseph A. Craig © 2003
|Where to next?|
If you think education is expensive, try ignorance. Derek Bok